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Potential speaker damage situation?

I'm using one of my bass cabs to play keys through (it's a custom made cab, no markings on the speaker). Using an M-Audio Prokeys 88sx with built in sounds. (this is a full 88 keyboard) Some of the tones have a built in tremolo function, adjustable for depth.

When I crank up the depth for the tremolo (on say a Wurlitzer tone), I see the speaker move in and out as the tremolo "breathes". I gotta admit, even at low volumes, it's a pretty decent amount of speaker travel, and I can only imagine what the speaker is doing when I'm playing louder.

I used a 1x10 cab as a monitor for an outdoor gig I played over the weekend (full PA support, including monitors - but wanted control over my own instrument volume that reached my ears). I don't think I blew it (seemed fine all night - but haven't tried it at home yet)... just worried about so much visible cone travel.
 
When I crank up the depth for the tremolo (on say a Wurlitzer tone), I see the speaker move in and out as the tremolo "breathes". I gotta admit, even at low volumes, it's a pretty decent amount of speaker travel, and I can only imagine what the speaker is doing when I'm playing louder.
That's probably the driver moving at the same frequency as the tremolo modulation, and yes, it could overtax both the driver and the amp. I'd add an 18dB/octave 30 Hz electronic high pass filter between the keyboard and the amp to filter out potentially damaging sub-sonic content.
 
If you want to do that permanently get the HPF from Francis Deck.

I hate to say it because he's a great guy, but for electric bass I think at least a 3rd order (18dB/octave) HPF is the way to roll. When appropriate rolloff frequency is selected a steeper filter cuts less into useful content and protects more against driver unloading.